CUGate

class qiskit.circuit.library.CUGate(theta, phi, lam, gamma, label=None, ctrl_state=None, *, duration=None, unit='dt', _base_label=None)

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Bases: ControlledGate

Controlled-U gate (4-parameter two-qubit gate).

This is a controlled version of the U gate (generic single qubit rotation), including a possible global phase $e^{i\gamma}$ of the U gate.

Can be applied to a QuantumCircuit with the cu() method.

Circuit symbol:

q_0: ──────■──────
     ┌─────┴──────┐
q_1: ┤ U(ϴ,φ,λ,γ) ├
     └────────────┘

Matrix representation:

\providecommand{\rotationangle}{\frac{\theta}{2}} CU(\theta, \phi, \lambda, \gamma)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + e^{i\gamma} U(\theta,\phi,\lambda) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{i\gamma}\cos(\rotationangle) & 0 & -e^{i(\gamma + \lambda)}\sin(\rotationangle) \\ 0 & 0 & 1 & 0 \\ 0 & e^{i(\gamma+\phi)}\sin(\rotationangle) & 0 & e^{i(\gamma+\phi+\lambda)}\cos(\rotationangle) \end{pmatrix}

Note

In Qiskit’s convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be:

     ┌────────────┐
q_0: ┤ U(ϴ,φ,λ,γ) ├
     └─────┬──────┘
q_1: ──────■───────

\providecommand{\rotationangle}{\frac{\theta}{2}} CU(\theta, \phi, \lambda, \gamma)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + e^{i\gamma}|1\rangle\langle 1| \otimes U(\theta,\phi,\lambda) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{i\gamma} \cos(\rotationangle) & -e^{i(\gamma + \lambda)}\sin(\rotationangle) \\ 0 & 0 & e^{i(\gamma + \phi)}\sin(\rotationangle) & e^{i(\gamma + \phi+\lambda)}\cos(\rotationangle) \end{pmatrix}

Create new CU gate.

Attributes

base_class

Get the base class of this instruction. This is guaranteed to be in the inheritance tree of self.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioural perspective. In particular, you should not override base_class if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrised gate with a particular set of parameters for the purposes of distinguishing it in a Target from the full parametrised gate.

This is often exactly equivalent to type(obj), except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

>>> isinstance(XGate(), XGate)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that Instruction.name should be a more suitable discriminator in most situations.

condition

The classical condition on the instruction.

condition_bits

Get Clbits in condition.

ctrl_state

Return the control state of the gate as a decimal integer.

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates. If the gate has open controls, as determined from self.ctrl_state, the returned definition is conjugated with X without changing the internal _definition.

duration

Get the duration.

label

Return instruction label

mutable

Is this instance is a mutable unique instance or not.

If this attribute is False the gate instance is a shared singleton and is not mutable.

name

Get name of gate. If the gate has open controls the gate name will become:

<original_name_o<ctrl_state>

where <original_name> is the gate name for the default case of closed control qubits and <ctrl_state> is the integer value of the control state for the gate.

num_clbits

Return the number of clbits.

num_ctrl_qubits

Get number of control qubits.

Returns

The number of control qubits for the gate.

Return type

int

num_qubits

Return the number of qubits.

params

unit

Get the time unit of duration.

Methods

inverse

inverse(annotated=False)

GitHub

Return inverted CU gate.

$CU(\theta,\phi,\lambda,\gamma)^{\dagger} = CU(-\theta,-\phi,-\lambda,-\gamma))$

Parameters

annotated (bool) – when set to True, this is typically used to return an AnnotatedOperation with an inverse modifier set instead of a concrete Gate. However, for this class this argument is ignored as the inverse of this gate is always a CUGate with inverse parameter values.

Returns

inverse gate.

Return type

CUGate

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